Hierarchical models, marginal polytopes, and linear codes

Thomas Kahle; Walter Wenzel; Nihat Ay

Kybernetika (2009)

  • Volume: 45, Issue: 2, page 189-207
  • ISSN: 0023-5954

Abstract

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In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.

How to cite

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Kahle, Thomas, Wenzel, Walter, and Ay, Nihat. "Hierarchical models, marginal polytopes, and linear codes." Kybernetika 45.2 (2009): 189-207. <http://eudml.org/doc/37728>.

@article{Kahle2009,
abstract = {In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.},
author = {Kahle, Thomas, Wenzel, Walter, Ay, Nihat},
journal = {Kybernetika},
keywords = {0/1 polytopes; linear codes; hierarchical models; exponential families; polytopes; linear codes; hierarchical models; exponential families},
language = {eng},
number = {2},
pages = {189-207},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Hierarchical models, marginal polytopes, and linear codes},
url = {http://eudml.org/doc/37728},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Kahle, Thomas
AU - Wenzel, Walter
AU - Ay, Nihat
TI - Hierarchical models, marginal polytopes, and linear codes
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 189
EP - 207
AB - In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.
LA - eng
KW - 0/1 polytopes; linear codes; hierarchical models; exponential families; polytopes; linear codes; hierarchical models; exponential families
UR - http://eudml.org/doc/37728
ER -

References

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